During the past decades, there has been an increasing interest in
the study of classical and quantum integrability of Heisenberg
ferromagnet (HM) model [1]}-[2]}. The
Heisenberg ferromagnet (HM) model based on Hermitian symmetric
spaces has been studied in [3]}-[4]}.
The integrability of the HM model based on \(SU(2)\)  via inverse
scattering method is presented in [5]}-[6]} and its
\(SU(n)\)  generalization is studied in [7]}. The
integrability of the GHM model based on the general linear Lie
group \(GL(n)\)  via Lax formalism has been investigated in
[1]}. In this paper we present the Darboux
transformation of the GHM model based on general linear group
\(GL(n)\)  with Lie algebra \({\tt gl(n)}\)  and calculate
multi-soliton solutions in term of quasideterminants. We also
establish the relation between the Darboux transformation and the
well-known dressing method [9]}. In the last section, we
discuss the model based \(SU(n)\)  and calculate an explicit
expression of the single-soliton solution of the HM model based on
the Lie group \(SU(2)\)  using Darboux transformation.
